Kraft Heinz is expanding a recall of Kraft Singles products, saying a problem with the packaging film affects 10 times as many cases as it first thought.

The company recalled 335,000 cases Thursday because a thin strip of packaging film may stick to the slice after the wrapper has been taken off, creating a choking hazard. Kraft Heinz took 36,000 cases off the market July 31 for the same reason.

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The privately-held company said it's received two new reports of customers choking. It disclosed three such reports in July.

The recall covers 1-, 3- and 4-pound Kraft Singles American and White American cheese product sold in the U.S., Puerto Rico, and 10 other countries and territories. The cases have "Best When Used by Dates" from Dec. 29 through Jan. 4.